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The golden ratio in architecture

The golden ratio in architecture. Kristijan Štefanec. The golden ratio. Also called φ Two quantities a and b are said to be in golden ratio if = = φ The second definition of φ is: φ -1= From this one, we can easily calculate φ : - φ -1=0 φ = ≈1.618

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The golden ratio in architecture

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  1. The golden ratio in architecture Kristijan Štefanec

  2. The golden ratio • Also called φ • Two quantities a and b are said to be in golden ratio if = =φ • The second definition of φ is: φ-1= • From this one, we can easily calculate φ: - φ-1=0 φ= ≈1.618 • Dymenzions of the Great Pyramid of Giza can be easily expressed by φ φ2

  3. Fibonacci series • Fibonacci was Italian mathematican from 13th century. • Numbers in Fibonacci series must satisfy this conditions:F0=0, F1=1 and: Fn=Fn-1+Fn-2 • The first few of them are: 0,1,1,2,3,5,8,13,21,34,55,89... • Fi/Fi-1≈φ and that ratio is more and more closer to φ as i rises.

  4. φ in art and architecture • Very important ratio in all arts and architecture • golden ratio was known even in ancient greece • for exemple here on parthenon we have many golden ratios • Even Mona Lisa has golden ratio:

  5. φ in architecture • In 15th century, first time called “God’s ratio” • Excelent examples for it are CN tower in Toronto and church Notre Damme • The height of the first level is 342 meters and the top is at 553.3 m so the ratio is: 553.3/342=1.618 • As we can see on picture, Notre Damme has many distances that are in golden ratio

  6. φ in Croatian architecture and Zagreb cathedral • There are plenty of buildings in Croatia with some dimensions in golden ratio • Probably the most important is chatedral in Zagreb • here are some of the golden ratios: • Also, the height of the towers and height of the main building are in gold ratio

  7. Cathedral • The Zagreb Cathedral on Kaptol is a Roman Catholic institution and one of the tallest buildings in Croatia. • Dedicated to the Assumption of Mary • Construction started in 1094 • Destroyed in 1242 by the Tatars • Rebuild and again destroyed in 1880 by earthquake • Restorated in Neo-Gothic style • 108 meters high

  8. Interesting facts • φ can be found even in Pascals triangle • in pentagon, φ iz the ratio between diagonal and two parts of diagonal that are made by intersecting the first diagonal with the second

  9. Twitter’s design was made in golden ratio • In pentagon, diagonals divide each others, creating 4 segments, as on the picture below • b/d=c/b=a/c=φ • Also, there are many places where we can find Fibonacci serie • For example, in Pascal’s triangle, where the sum of numbers on each diagonal gives one number from Fibonacci serie

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